A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method. The method uses a polynomial of one less degree than the full approximation to calculate the rst derivative so that interface values can be calculate...

This paper deals with the combination of two solution methods: multigrid and GMRES [SIAM J. Sci. Comput., 14 (1993), pp. 856–869]. The generality and parallelizability of this combination are established by applying it to systems of nonlinear PDEs. As the “preconditioner” for a nonlinear Krylov subspace method, we use the full approximation storage (FAS) scheme [Math. Comp., 31 (1977), pp. 333–...

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a model's dynamics over a large parameter space renders full-fledged stochastic simulations impractical, motivating approximation schemes. Here we propose an approximation scheme which improves upon the stand...

For European plain vanilla options, we investigate the difference between solutions obtained by the full-scale and an approximate Heston-Hull-White (HHW) model. Based on the corresponding two option pricing PDEs, we analyze the quality of the approximation. To confirm the accuracy of the analysis, we solve the HHW PDE, its approximating PDE as well as the PDE for the error, numerically, via a s...

A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step. This decomposition is obtained through the use of an efficient modified Progressive Generalized Decomposition (PGD) method, whose convergence is proved. We sug...

In the Min $k$-Cut problem, input consists of an edge weighted graph $G$ and integer $k$, task is to partition vertex set into $k$ nonempty sets, such that total weight edges with endpoints in different parts minimized. When part input, problem NP-complete hard approximate within any factor less than 2. Recently, has received significant attention from perspective parameterized approximation. G...